How do i find the partial derivative in terms of Y from the equation z = x^y even if X is held as a constant i dont know how to differentiate it :S
Follow these steps, where $\displaystyle z_y$ means the derivative of z with respect of y.
$\displaystyle \displaystyle{z=x^y}$
$\displaystyle \displaystyle{ln(z) = y\cdot ln(x)}$
$\displaystyle \displaystyle{\frac{\partial}{\partial y} ln (z) = \frac{\partial}{\partial y}\left(y\cdot ln (x)\right)}$
$\displaystyle \displaystyle{\frac{z_y}{z} = ln (x)}$
$\displaystyle \displaystyle{z_y = z\cdot ln (x) = x^y\cdot ln (x)}$
Got it?